MA2DENU: Differential Equations

Module code: MA2DENU

Module provider: Mathematics and Statistics; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: Level 2 (Intermediate)

When you'll be taught: Semester 1

Module convenor: Dr Peter Sweby, email: p.k.sweby@reading.ac.uk

NUIST module lead: Vahid Darvish, email: vdarvish@gmail.com

Pre-requisite module(s): BEFORE TAKING THIS MODULE YOU MUST TAKE MA0MANU AND TAKE MA1LANU AND TAKE MA1DE1NU (Compulsory)

Co-requisite module(s):

Pre-requisite or Co-requisite module(s):

Module(s) excluded:

Placement information: NA

Academic year: 2024/5

Available to visiting students: No

Talis reading list: No

Last updated: 21 May 2024

Overview

Module aims and purpose

This module is designed to teach students of mathematics a brief introduction to partial differential equations. What students learn in the class could be helpful for them in subsequent courses and research as well as in their career and in life in the long run.  This module is intended to teach students of mathematics fundamental knowledge of partial differential equations.

Module learning outcomes

By the end of the module, it is expected that students will be able to:

1. Classify 2nd order partial differential equations.
2. State and apply maximum principles to conclude uniqueness results.
3. Solve a variety of PDE IVP, BVP and IBVP problems, including for the diffusion equation, the wave equation and Laplace’s equation using appropriate techniques.

Module content

• Overview of PDEs; Classification of 2nd order partial differential equations; Conservation laws; First order linear equations; Laplace Transform,
• Method of the characteristics; the inviscid Burgers' equation.
• The Heat Equation on whole line and half-line, the heat kernel and Duhamel's principle.
• The Wave equation, including derivation, D' Alembert's formula and causality. The Wave equation on a finite and semi-infinite interval.
• Laplace's equation on rectangles, cubes, the exterior of circles, wedges, annuli and on a ball.
• The Poison Equation. Green's identities and Green's function
• Maximum principles.
• Separation of variables for the heat, wave and Laplace's equations on finite spatial regions.

Structure

Teaching and learning methods

Lectures, supported by non-assessed problem sheets, weekly tutorials, computer demonstrations and exercises.

Study hours

At least 54 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.

Please note the independent study hours above are notional numbers of hours; each student will approach studying in different ways. We would advise you to reflect on your learning and the number of hours you are allocating to these tasks.

Semester 1 The hours in this column may include hours during the Christmas holiday period.

Semester 2 The hours in this column may include hours during the Easter holiday period.

Summer The hours in this column will take place during the summer holidays and may be at the start and/or end of the module.

Assessment

Requirements for a pass

Students need to achieve an overall module mark of 40% to pass this module.

Summative assessment

Penalties for late submission of summative assessment

The Support Centres will apply the following penalties for work submitted late:

Assessments with numerical marks

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of three working days;
• the mark awarded due to the imposition of the penalty shall not fall below the threshold pass mark, namely 40% in the case of modules at Levels 4-6 (i.e. undergraduate modules for Parts 1-3) and 50% in the case of Level 7 modules offered as part of an Integrated Masters or taught postgraduate degree programme;
• where the piece of work is awarded a mark below the threshold pass mark prior to any penalty being imposed, and is submitted up to three working days after the original deadline (or any formally agreed extension to the deadline), no penalty shall be imposed;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three working days of the deadline (or any formally agreed extension of the deadline): no penalty will be applied;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension of the deadline): a grade of Fail will be awarded.

The University policy statement on penalties for late submission can be found at: /cqsd/-/media/project/functions/cqsd/documents/qap/penaltiesforlatesubmission.pdf

You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Formative assessment

Formative assessment is any task or activity which creates feedback (or feedforward) for you about your learning, but which does not contribute towards your overall module mark.

Reassessment

Additional costs